Real-time modelling and forecasting
of infectious disease dynamics


Sebastian Funk
8 March, 2018
Centre for Complex Systems Studies, Utrecht

Summer 2014

\(y=ax+b\)

\begin{eqnarray} \dot{S}&=&-\beta \frac{S}{N}I\\ \dot{I}&=&+\beta \frac{S}{N}I - \gamma I\\ \dot{R}&=&+\gamma I \end{eqnarray}

\(y=ax+b\)

"[…], Liberia and Sierra Leone will have approximately 550,000 Ebola cases (1.4 million when corrected for underreporting)"

Meltzer, 2014

What really happened

"[…], Liberia and Sierra Leone will have approximately 550,000 Ebola cases (1.4 million when corrected for underreporting)"

Meltzer, 2014

"without additional interventions or changes in community behavior (e.g., notable reductions in unsafe burial practices), the model also estimates that Liberia and Sierra Leone will have approximately 550,000 Ebola cases (1.4 million…)"

Meltzer, 2014

"A CDC model […] was key to increasing the speed and scale of the US and global response.

Frieden, 2015

Key findings:

  1. "cases were increasing exponentially, and the response needed was massive and urgent"
  2. "the model predicted a severe penalty for delay"
  3. "the model identified a tipping point at which the epidemic would [..] decline if enough Ebola patients were isolated effectively and decedents buried safely"
  4. "the model predicted that when the tipping point was reached, transmission would decline rapidly"

courtesy of Samuel V. Scarpino @svscarpino

Uses of real-time forecasts in outbreaks

  • Plan the scale of a response or intervention
  • Allocate resources (e.g., geographically)
  • Plan clinical trials

Metcalf & Lessler (2017)

A semi-mechanistic model for real-time forecasting

The unknown

  • Community/hospital/funeral transmission
  • Spatial dynamics
  • Changes in behaviour
  • Changes in reporting
  • Interventions
  • Seasonality
  • etc

The known

  • Average incubation period (~9 days)
  • Average infectious period (~11 days)
  • Case-fatality rate (~70%)

WHO Ebola response team (2014)

Transmission intensity as a stochastic process

\(d\log(R_0(t)) = \sigma dW_t\)

Dureau (2013)

Particle MCMC

  • Method for filtering trajectories consistent with data
  • Highly parallelisable

Andrieu (2010), Murray (2013)

Forecasting the Ebola epidemic

Assessing forecasts

Meaningful forecasts are probabilistic.

Meaningful forecasts are probabilistic.

Evaluating probabilistic forecasts requires
multiple observations.

Reliability plot

Reliability plot

Reliability plot

Reliability plot

Calibration: Compatibility of forecasts and observations.

Calibration: Compatibility of forecasts and observations.

Calibration: Compatibility of forecasts and observations.

"Evaluate predictive performance on the basis of maximising the sharpness of the predictive distribution subject to calibration"

Gneiting et al., J R Stat Soc B (2007)

Sharpness

Quality of forecasts vs quality of decisions

Outlook

Forecasts are becoming part of outbreak response

Forecasting challenges

Forecasting methodology is underdeveloped

Need methods to select the best model and
combine all available data streams
(individual/spatial/genetic/media)

Louis du Plessis, University of Oxford (unpublished)

New tools

New tools

Bayesian inference with state-space models in R

Summary

  • Real-time forecasts can aid decision making
  • Meaningful forecasts are probabilistic
  • Forecasts must be evaluated to establish reliability and limitations
  • Some big challenges remain

Acknowledgements

Anton Camacho, Adam Kucharski, Roz Eggo, John Edmunds (LSHTM)
Bruce Reeder, Etienne Gignoux, Iza Ciglenecki, Amanda Tiffany (MSF)
James Hensman (Lancaster), Lawrence Murray (Uppsala)

Thank you!

http://sbfnk.github.io
@sbfnk